We are fans of Sun Valley also. I agree with the Park City and Steamboat suggestions and, if you are willing to go up some in elevation, Snowmass along with the separate beginner hill at Buttermilk tick all the boxes.

It's not Colorado/Utah, but Timberline in Oregon might be worth considering--Portland's a big enough airport that flights shouldn't be a problem from most parts of the country, at least. Weekdays, at least, it should be very uncrowded; the lodge is really charming and has a big game room if the kids need distracting; and the elevation is about the same as Sun Valley. It's a very mellow ski area with fairly gentle terrain. I have no experience with their ski school--someone else on here probably does, though, if you're interested

You said you loved SV for it's "kids mountain"--so you must mean Dollar? If so, maybe Aspen would be good for you. It's a nice town, and my understanding is that Buttermilk is a learner's mountain (can someone from Aspen confirm?) with a big kids' ski school and the park/pipe, so it sounds a lot like Dollar to me.

Neither Steamboat or Park City remind me of SV. They have the lower elevations, but they both feel a lot more crowded to me (esp Park City). Though maybe since you aren't going to find someplace exactly like SV, they might still meet your needs.

Have you ever flown into Boise? It's such an easy 2:40 drive (and that's going the "winter way" via Hwy 26) to Sun Valley. We just did it this weekend. But I know it can also be hard to get to Boise if you are east of the Mississippi.

I'd also consider Jackson if you all are upper intermediate skiers, if you can ski baldy you will be able to ski enough in jh to have a lot of fun, and I always see the kids having a lot of fun either with family or instructors!